Question

Given \( f(x, y)=-6 x^{3}-5 x^{2} y^{4}-4 y^{2} \), find \[ f_{x}(x, y)= \] \( \square \) \[ f_{y}(x, y)= \] \( \square \) \[ f_{x x}(x, y)= \] \( \square \) \[ f_{x y}(x, y)= \] \( \square \)

          Given \( f(x, y)=-6 x^{3}-5 x^{2} y^{4}-4 y^{2} \), find
\[
f_{x}(x, y)=
\]
\( \square \)
\[
f_{y}(x, y)=
\]
\( \square \)
\[
f_{x x}(x, y)=
\]
\( \square \)
\[
f_{x y}(x, y)=
\]
\( \square \)

Given f(x, y)=-6 x^3-5 x^2 y^4-4 y^2, find

fx(x, y)=

□

fy(x, y)=

□

fx x(x, y)=

□

fx y(x, y)=

□

Added by Teodora B.

Calculus A New Horizon

Howard Anton 6th Edition

Chapter 15

Instant Answer

Solved by Expert Eleni Katirtzoglou

Step 1

- Start by differentiating each term of \( f(x, y) = -6x^3 - 5x^2y^4 - 4y^2 \) with respect to \( x \). - The derivative of \(-6x^3\) with respect to \( x \) is \(-18x^2\). - The derivative of \(-5x^2y^4\) with respect to \( x \) is \(-10xy^4\) (using the power Show more…

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